LMFDB - Embedded newform 783.2.k.f.136.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(82,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.k (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0,-10,0,0,4,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			136.5
Character	$\chi$	$=$	783.136
Dual form			783.2.k.f.190.5

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0355415 + 0.0171159i) q^{2} +(-1.24601 + 1.56245i) q^{4} +(2.93813 - 1.41493i) q^{5} +(1.13234 + 1.41991i) q^{7} +(0.0350984 - 0.153776i) q^{8} +(-0.0802077 + 0.100577i) q^{10} +(0.113002 + 0.495093i) q^{11} +(0.503606 + 2.20644i) q^{13} +(-0.0645483 - 0.0310848i) q^{14} +(-0.888007 - 3.89061i) q^{16} +3.49545 q^{17} +(0.112911 - 0.141586i) q^{19} +(-1.45019 + 6.35368i) q^{20} +(-0.0124902 - 0.0156622i) q^{22} +(0.599645 + 0.288774i) q^{23} +(3.51313 - 4.40532i) q^{25} +(-0.0556641 - 0.0698006i) q^{26} -3.62945 q^{28} +(0.790993 + 5.32676i) q^{29} +(-3.29319 + 1.58592i) q^{31} +(0.294840 + 0.369717i) q^{32} +(-0.124233 + 0.0598277i) q^{34} +(5.33605 + 2.56971i) q^{35} +(0.985051 - 4.31579i) q^{37} +(-0.00158966 + 0.00696476i) q^{38} +(-0.114459 - 0.501476i) q^{40} +5.34511 q^{41} +(-2.69372 - 1.29723i) q^{43} +(-0.914357 - 0.440331i) q^{44} -0.0262549 q^{46} +(2.81182 + 12.3194i) q^{47} +(0.823692 - 3.60883i) q^{49} +(-0.0494608 + 0.216702i) q^{50} +(-4.07495 - 1.96239i) q^{52} +(-1.46623 + 0.706101i) q^{53} +(1.03253 + 1.29476i) q^{55} +(0.258093 - 0.124291i) q^{56} +(-0.119285 - 0.175782i) q^{58} +8.32033 q^{59} +(6.31949 + 7.92439i) q^{61} +(0.0899006 - 0.112732i) q^{62} +(7.17412 + 3.45488i) q^{64} +(4.60162 + 5.77025i) q^{65} +(-0.903434 + 3.95820i) q^{67} +(-4.35536 + 5.46145i) q^{68} -0.233634 q^{70} +(-3.04623 - 13.3464i) q^{71} +(-3.15028 - 1.51709i) q^{73} +(0.0388584 + 0.170250i) q^{74} +(0.0805324 + 0.352836i) q^{76} +(-0.575033 + 0.721068i) q^{77} +(-2.73209 + 11.9701i) q^{79} +(-8.11401 - 10.1747i) q^{80} +(-0.189973 + 0.0914862i) q^{82} +(-1.64649 + 2.06464i) q^{83} +(10.2701 - 4.94581i) q^{85} +0.117942 q^{86} +0.0800997 q^{88} +(9.78397 - 4.71171i) q^{89} +(-2.56270 + 3.21353i) q^{91} +(-1.19836 + 0.577098i) q^{92} +(-0.310794 - 0.389723i) q^{94} +(0.131413 - 0.575760i) q^{95} +(-4.88308 + 6.12319i) q^{97} +(0.0324931 + 0.142361i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 10 q^{4} + 4 q^{7} + 4 q^{10} - 24 q^{13} - 26 q^{16} + 4 q^{19} - 8 q^{22} - 16 q^{25} + 112 q^{28} - 4 q^{31} + 26 q^{34} - 18 q^{37} - 78 q^{40} - 8 q^{43} + 72 q^{46} + 14 q^{49} - 12 q^{52}+ \cdots + 8 q^{97}+O(q^{100}) $ 60 * q - 10 * q^4 + 4 * q^7 + 4 * q^10 - 24 * q^13 - 26 * q^16 + 4 * q^19 - 8 * q^22 - 16 * q^25 + 112 * q^28 - 4 * q^31 + 26 * q^34 - 18 * q^37 - 78 * q^40 - 8 * q^43 + 72 * q^46 + 14 * q^49 - 12 * q^52 + 24 * q^55 - 162 * q^58 - 10 * q^61 + 116 * q^64 + 60 * q^67 - 12 * q^70 + 66 * q^73 - 120 * q^76 + 46 * q^79 - 84 * q^82 - 122 * q^85 - 152 * q^88 - 30 * q^91 - 68 * q^94 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0355415	+	0.0171159i	−0.0251316	+	0.0121028i	−0.446407	−	0.894830i	$-0.647297\pi$
$2$	−0.0355415	+	0.0171159i	−0.0251316	+	0.0121028i	0.421276	+	0.906933i	$0.361582\pi$
$3$		0			0
$3$		0			0
$4$	−1.24601	+	1.56245i	−0.623005	+	0.781223i
$5$	2.93813	−	1.41493i	1.31397	−	0.632775i	0.360078	−	0.932922i	$-0.382750\pi$
$5$	2.93813	−	1.41493i	1.31397	−	0.632775i	0.953893	+	0.300147i	$0.0970357\pi$
$6$		0			0
$7$	1.13234	+	1.41991i	0.427986	+	0.536677i	0.948333	−	0.317278i	$-0.102769\pi$
$7$	1.13234	+	1.41991i	0.427986	+	0.536677i	−0.520347	+	0.853955i	$0.674197\pi$
$8$	0.0350984	−	0.153776i	0.0124092	−	0.0543681i
$9$		0			0
$10$	−0.0802077	+	0.100577i	−0.0253639	+	0.0318053i
$11$	0.113002	+	0.495093i	0.0340713	+	0.149276i	0.989102	−	0.147230i	$-0.0470357\pi$
$11$	0.113002	+	0.495093i	0.0340713	+	0.149276i	−0.955031	+	0.296506i	$0.904179\pi$
$12$		0			0
$13$	0.503606	+	2.20644i	0.139675	+	0.611957i	0.995506	+	0.0947008i	$0.0301894\pi$
$13$	0.503606	+	2.20644i	0.139675	+	0.611957i	−0.855831	+	0.517256i	$0.826953\pi$
$14$	−0.0645483	−	0.0310848i	−0.0172513	−	0.00830777i
$15$		0			0
$16$	−0.888007	−	3.89061i	−0.222002	−	0.972653i
$17$	3.49545			0.847771			0.423885	−	0.905716i	$-0.360666\pi$
$17$	3.49545			0.847771			0.423885	+	0.905716i	$0.360666\pi$
$18$		0			0
$19$	0.112911	−	0.141586i	0.0259036	−	0.0324821i	−0.768711	−	0.639596i	$-0.779102\pi$
$19$	0.112911	−	0.141586i	0.0259036	−	0.0324821i	0.794615	+	0.607114i	$0.207673\pi$
$20$	−1.45019	+	6.35368i	−0.324272	+	1.42073i
$21$		0			0
$22$	−0.0124902	−	0.0156622i	−0.00266292	−	0.00333919i
$23$	0.599645	+	0.288774i	0.125035	+	0.0602135i	0.495355	−	0.868690i	$-0.335038\pi$
$23$	0.599645	+	0.288774i	0.125035	+	0.0602135i	−0.370321	+	0.928904i	$0.620752\pi$
$24$		0			0
$25$	3.51313	−	4.40532i	0.702626	−	0.881065i
$26$	−0.0556641	−	0.0698006i	−0.0109166	−	0.0136890i
$27$		0			0
$28$	−3.62945			−0.685902
$29$	0.790993	+	5.32676i	0.146884	+	0.989154i
$29$	0.790993	+	5.32676i	0.146884	+	0.989154i
$30$		0			0
$31$	−3.29319	+	1.58592i	−0.591475	+	0.284839i	−0.705581	−	0.708629i	$-0.749314\pi$
$31$	−3.29319	+	1.58592i	−0.591475	+	0.284839i	0.114106	+	0.993469i	$0.463600\pi$
$32$	0.294840	+	0.369717i	0.0521208	+	0.0653574i
$33$		0			0
$34$	−0.124233	+	0.0598277i	−0.0213059	+	0.0102604i
$35$	5.33605	+	2.56971i	0.901957	+	0.434360i
$36$		0			0
$37$	0.985051	−	4.31579i	0.161941	−	0.709511i	−0.827122	−	0.562022i	$-0.810024\pi$
$37$	0.985051	−	4.31579i	0.161941	−	0.709511i	0.989064	−	0.147489i	$-0.0471192\pi$
$38$	−0.00158966	+	0.00696476i	−0.000257877	+	0.00112983i
$39$		0			0
$40$	−0.114459	−	0.501476i	−0.0180975	−	0.0792904i
$41$	5.34511			0.834765			0.417383	−	0.908731i	$-0.362947\pi$
$41$	5.34511			0.834765			0.417383	+	0.908731i	$0.362947\pi$
$42$		0			0
$43$	−2.69372	−	1.29723i	−0.410789	−	0.197826i	0.217064	−	0.976157i	$-0.430352\pi$
$43$	−2.69372	−	1.29723i	−0.410789	−	0.197826i	−0.627853	+	0.778332i	$0.716066\pi$
$44$	−0.914357	−	0.440331i	−0.137844	−	0.0663824i
$45$		0			0
$46$	−0.0262549			−0.00387107
$47$	2.81182	+	12.3194i	0.410147	+	1.79697i	0.583504	+	0.812110i	$0.301681\pi$
$47$	2.81182	+	12.3194i	0.410147	+	1.79697i	−0.173357	+	0.984859i	$0.555462\pi$
$48$		0			0
$49$	0.823692	−	3.60883i	0.117670	−	0.515547i
$50$	−0.0494608	+	0.216702i	−0.00699482	+	0.0306463i
$51$		0			0
$52$	−4.07495	−	1.96239i	−0.565093	−	0.272135i
$53$	−1.46623	+	0.706101i	−0.201403	+	0.0969905i	−0.531866	−	0.846828i	$-0.678509\pi$
$53$	−1.46623	+	0.706101i	−0.201403	+	0.0969905i	0.330464	+	0.943819i	$0.392795\pi$
$54$		0			0
$55$	1.03253	+	1.29476i	0.139227	+	0.174585i
$56$	0.258093	−	0.124291i	0.0344891	−	0.0166091i
$57$		0			0
$58$	−0.119285	−	0.175782i	−0.0156629	−	0.0230813i
$59$	8.32033			1.08321			0.541607	−	0.840632i	$-0.317816\pi$
$59$	8.32033			1.08321			0.541607	+	0.840632i	$0.317816\pi$
$60$		0			0
$61$	6.31949	+	7.92439i	0.809128	+	1.01461i	0.999459	+	0.0328947i	$0.0104726\pi$
$61$	6.31949	+	7.92439i	0.809128	+	1.01461i	−0.190331	+	0.981720i	$0.560956\pi$
$62$	0.0899006	−	0.112732i	0.0114174	−	0.0143170i
$63$		0			0
$64$	7.17412	+	3.45488i	0.896765	+	0.431859i
$65$	4.60162	+	5.77025i	0.570760	+	0.715711i
$66$		0			0
$67$	−0.903434	+	3.95820i	−0.110372	+	0.483571i	0.889284	+	0.457355i	$0.151203\pi$
$67$	−0.903434	+	3.95820i	−0.110372	+	0.483571i	−0.999656	+	0.0262165i	$0.991654\pi$
$68$	−4.35536	+	5.46145i	−0.528165	+	0.662298i
$69$		0			0
$70$	−0.233634			−0.0279246
$71$	−3.04623	−	13.3464i	−0.361521	−	1.58393i	−0.749337	−	0.662189i	$-0.769628\pi$
$71$	−3.04623	−	13.3464i	−0.361521	−	1.58393i	0.387816	−	0.921737i	$-0.373230\pi$
$72$		0			0
$73$	−3.15028	−	1.51709i	−0.368712	−	0.177562i	0.240347	−	0.970687i	$-0.422739\pi$
$73$	−3.15028	−	1.51709i	−0.368712	−	0.177562i	−0.609059	+	0.793125i	$0.708453\pi$
$74$	0.0388584	+	0.170250i	0.00451719	+	0.0197911i
$75$		0			0
$76$	0.0805324	+	0.352836i	0.00923770	+	0.0404730i
$77$	−0.575033	+	0.721068i	−0.0655310	+	0.0821733i
$78$		0			0
$79$	−2.73209	+	11.9701i	−0.307384	+	1.34674i	0.551332	+	0.834286i	$0.314120\pi$
$79$	−2.73209	+	11.9701i	−0.307384	+	1.34674i	−0.858716	+	0.512451i	$0.828738\pi$
$80$	−8.11401	−	10.1747i	−0.907174	−	1.13756i
$81$		0			0
$82$	−0.189973	+	0.0914862i	−0.0209790	+	0.0101030i
$83$	−1.64649	+	2.06464i	−0.180726	+	0.226623i	−0.863940	−	0.503595i	$-0.832010\pi$
$83$	−1.64649	+	2.06464i	−0.180726	+	0.226623i	0.683214	+	0.730219i	$0.260582\pi$
$84$		0			0
$85$	10.2701	−	4.94581i	1.11395	−	0.536448i
$86$	0.117942			0.0127180
$87$		0			0
$88$	0.0800997			0.00853865
$89$	9.78397	−	4.71171i	1.03710	−	0.499440i	0.163732	−	0.986505i	$-0.447647\pi$
$89$	9.78397	−	4.71171i	1.03710	−	0.499440i	0.873366	+	0.487065i	$0.161932\pi$
$90$		0			0
$91$	−2.56270	+	3.21353i	−0.268644	+	0.336869i
$92$	−1.19836	+	0.577098i	−0.124937	+	0.0601667i
$93$		0			0
$94$	−0.310794	−	0.389723i	−0.0320559	−	0.0401969i
$95$	0.131413	−	0.575760i	0.0134827	−	0.0590717i
$96$		0			0
$97$	−4.88308	+	6.12319i	−0.495802	+	0.621716i	−0.965277	−	0.261230i	$-0.915872\pi$
$97$	−4.88308	+	6.12319i	−0.495802	+	0.621716i	0.469475	+	0.882946i	$0.344443\pi$
$98$	0.0324931	+	0.142361i	0.00328230	+	0.0143807i
$99$		0			0
$100$	2.50569	+	10.9782i	0.250569	+	1.09782i
$101$	−5.83094	−	2.80803i	−0.580200	−	0.279410i	0.120677	−	0.992692i	$-0.461493\pi$
$101$	−5.83094	−	2.80803i	−0.580200	−	0.279410i	−0.700877	+	0.713282i	$0.747208\pi$
$102$		0			0
$103$	−1.08979	−	4.77468i	−0.107380	−	0.470463i	−0.999814	−	0.0192850i	$-0.993861\pi$
$103$	−1.08979	−	4.77468i	−0.107380	−	0.470463i	0.892434	−	0.451178i	$-0.148996\pi$
$104$	0.356974			0.0350042
$105$		0			0
$106$	0.0400266	−	0.0501918i	0.00388773	−	0.00487506i
$107$	1.66104	−	7.27749i	0.160579	−	0.703542i	−0.828964	−	0.559302i	$-0.811069\pi$
$107$	1.66104	−	7.27749i	0.160579	−	0.703542i	0.989543	−	0.144240i	$-0.0460736\pi$
$108$		0			0
$109$	−9.16120	−	11.4878i	−0.877484	−	1.10033i	−0.994241	−	0.107170i	$-0.965821\pi$
$109$	−9.16120	−	11.4878i	−0.877484	−	1.10033i	0.116757	−	0.993161i	$-0.462750\pi$
$110$	−0.0588587	−	0.0283449i	−0.00561196	−	0.00270258i
$111$		0			0
$112$	4.51881	−	5.66640i	0.426987	−	0.535425i
$113$	−10.6404	−	13.3426i	−1.00096	−	1.25517i	−0.966742	−	0.255755i	$-0.917676\pi$
$113$	−10.6404	−	13.3426i	−1.00096	−	1.25517i	−0.0342220	−	0.999414i	$-0.510895\pi$
$114$		0			0
$115$	2.17043			0.202393
$116$	−9.30835	−	5.40130i	−0.864259	−	0.501498i
$117$		0			0
$118$	−0.295717	+	0.142410i	−0.0272229	+	0.0131099i
$119$	3.95805	+	4.96324i	0.362834	+	0.454979i
$120$		0			0
$121$	9.67831	−	4.66083i	0.879846	−	0.423712i
$122$	−0.360237	−	0.173481i	−0.0326143	−	0.0157062i
$123$		0			0
$124$	1.62544	−	7.12151i	0.145969	−	0.639530i
$125$	0.460518	−	2.01766i	0.0411900	−	0.180465i
$126$		0			0
$127$	−0.646515	−	2.83257i	−0.0573689	−	0.251350i	0.938109	−	0.346339i	$-0.112575\pi$
$127$	−0.646515	−	2.83257i	−0.0573689	−	0.251350i	−0.995478	+	0.0949895i	$0.969718\pi$
$128$	−1.25988			−0.111359
$129$		0			0
$130$	−0.262311	−	0.126322i	−0.0230062	−	0.0110792i
$131$	−10.2587	−	4.94035i	−0.896310	−	0.431640i	−0.0717553	−	0.997422i	$-0.522860\pi$
$131$	−10.2587	−	4.94035i	−0.896310	−	0.431640i	−0.824555	+	0.565782i	$0.808574\pi$
$132$		0			0
$133$	0.328895			0.0285188
$134$	−0.0356387	−	0.156143i	−0.00307872	−	0.0134887i
$135$		0			0
$136$	0.122685	−	0.537517i	0.0105201	−	0.0460917i
$137$	3.08595	−	13.5204i	0.263651	−	1.15513i	−0.653607	−	0.756834i	$-0.726745\pi$
$137$	3.08595	−	13.5204i	0.263651	−	1.15513i	0.917257	−	0.398295i	$-0.130398\pi$
$138$		0			0
$139$	−16.8379	−	8.10869i	−1.42817	−	0.687770i	−0.449513	−	0.893274i	$-0.648402\pi$
$139$	−16.8379	−	8.10869i	−1.42817	−	0.687770i	−0.978656	+	0.205504i	$0.934117\pi$
$140$	−10.6638	+	5.13541i	−0.901255	+	0.434022i
$141$		0			0
$142$	0.336703	+	0.422212i	0.0282555	+	0.0354312i
$143$	−1.03549	+	0.498663i	−0.0865916	+	0.0417003i
$144$		0			0
$145$	9.86102	+	14.5315i	0.818913	+	1.20678i
$146$	0.137932			0.0114153
$147$		0			0
$148$	5.51581	+	6.91660i	0.453396	+	0.568541i
$149$	−5.47075	+	6.86010i	−0.448181	+	0.562001i	−0.953679	−	0.300826i	$-0.902737\pi$
$149$	−5.47075	+	6.86010i	−0.448181	+	0.562001i	0.505498	+	0.862828i	$0.331309\pi$
$150$		0			0
$151$	−19.6929	−	9.48362i	−1.60259	−	0.771766i	−0.602927	−	0.797796i	$-0.705999\pi$
$151$	−19.6929	−	9.48362i	−1.60259	−	0.771766i	−0.999661	+	0.0260301i	$0.991713\pi$
$152$	−0.0178096	−	0.0223325i	−0.00144455	−	0.00181141i
$153$		0			0
$154$	0.00809580	−	0.0354700i	0.000652378	−	0.00285826i
$155$	−7.43186	+	9.31926i	−0.596942	+	0.748541i
$156$		0			0
$157$	−11.9300			−0.952117			−0.476058	−	0.879414i	$-0.657935\pi$
$157$	−11.9300			−0.952117			−0.476058	+	0.879414i	$0.657935\pi$
$158$	−0.107776	−	0.472196i	−0.00857417	−	0.0375659i
$159$		0			0
$160$	1.38940	+	0.669100i	0.109842	+	0.0528970i
$161$	0.268970	+	1.17844i	0.0211978	+	0.0928738i
$162$		0			0
$163$	−1.88347	−	8.25202i	−0.147525	−	0.646348i	−0.993568	−	0.113234i	$-0.963879\pi$
$163$	−1.88347	−	8.25202i	−0.147525	−	0.646348i	0.846044	−	0.533114i	$-0.178978\pi$
$164$	−6.66005	+	8.35144i	−0.520063	+	0.652138i
$165$		0			0
$166$	0.0231807	−	0.101561i	0.00179917	−	0.00788270i
$167$	−4.58584	−	5.75046i	−0.354863	−	0.444984i	0.572074	−	0.820202i	$-0.306139\pi$
$167$	−4.58584	−	5.75046i	−0.354863	−	0.444984i	−0.926936	+	0.375218i	$0.877568\pi$
$168$		0			0
$169$	7.09783	−	3.41813i	0.545987	−	0.262933i
$170$	−0.280362	+	0.351563i	−0.0215028	+	0.0269636i
$171$		0			0
$172$	5.38326	−	2.59244i	0.410470	−	0.197672i
$173$	23.7159			1.80309			0.901543	−	0.432689i	$-0.142435\pi$
$173$	23.7159			1.80309			0.901543	+	0.432689i	$0.142435\pi$
$174$		0			0
$175$	10.2333			0.773562
$176$	1.82587	−	0.879291i	0.137630	−	0.0662791i
$177$		0			0
$178$	−0.267092	+	0.334922i	−0.0200194	+	0.0251035i
$179$	21.5888	−	10.3966i	1.61362	−	0.777079i	0.613699	−	0.789540i	$-0.289681\pi$
$179$	21.5888	−	10.3966i	1.61362	−	0.777079i	0.999922	+	0.0124613i	$0.00396666\pi$
$180$		0			0
$181$	−11.6232	−	14.5751i	−0.863947	−	1.08336i	−0.995752	−	0.0920797i	$-0.970649\pi$
$181$	−11.6232	−	14.5751i	−0.863947	−	1.08336i	0.131805	−	0.991276i	$-0.457923\pi$
$182$	0.0360800	−	0.158077i	0.00267442	−	0.0117174i
$183$		0			0
$184$	0.0654532	−	0.0820757i	0.00482527	−	0.00605070i
$185$	−3.21233	−	14.0741i	−0.236175	−	1.03475i
$186$		0			0
$187$	0.394991	+	1.73057i	0.0288846	+	0.126552i
$188$	−22.7520	−	10.9568i	−1.65936	−	0.799104i
$189$		0			0
$190$	0.00518401	+	0.0227126i	0.000376088	+	0.00164775i
$191$	−21.0544			−1.52344			−0.761722	−	0.647904i	$-0.775646\pi$
$191$	−21.0544			−1.52344			−0.761722	+	0.647904i	$0.775646\pi$
$192$		0			0
$193$	−8.15888	+	10.2309i	−0.587289	+	0.736437i	−0.983337	−	0.181793i	$-0.941810\pi$
$193$	−8.15888	+	10.2309i	−0.587289	+	0.736437i	0.396048	+	0.918230i	$0.370381\pi$
$194$	0.0687482	−	0.301206i	0.00493583	−	0.0216253i
$195$		0			0
$196$	4.61228	+	5.78361i	0.329448	+	0.413115i
$197$	11.9773	+	5.76798i	0.853350	+	0.410951i	0.808820	−	0.588057i	$-0.200107\pi$
$197$	11.9773	+	5.76798i	0.853350	+	0.410951i	0.0445298	+	0.999008i	$0.485821\pi$
$198$		0			0
$199$	−0.802831	+	1.00672i	−0.0569112	+	0.0713643i	−0.809472	−	0.587158i	$-0.800247\pi$
$199$	−0.802831	+	1.00672i	−0.0569112	+	0.0713643i	0.752561	+	0.658522i	$0.228818\pi$
$200$	−0.554129	−	0.694856i	−0.0391828	−	0.0491337i
$201$		0			0
$202$	0.255302			0.0179630
$203$	−6.66786	+	7.15486i	−0.467992	+	0.502173i
$204$		0			0
$205$	15.7046	−	7.56294i	1.09686	−	0.528219i
$206$	0.120456	+	0.151047i	0.00839254	+	0.0105239i
$207$		0			0
$208$	8.13720	−	3.91867i	0.564214	−	0.271711i
$209$	0.0828575	+	0.0399021i	0.00573137	+	0.00276008i
$210$		0			0
$211$	−2.27753	+	9.97850i	−0.156792	+	0.686949i	0.834024	+	0.551728i	$0.186031\pi$
$211$	−2.27753	+	9.97850i	−0.156792	+	0.686949i	−0.990816	+	0.135220i	$0.956826\pi$
$212$	0.723697	−	3.17072i	0.0497037	−	0.217766i
$213$		0			0
$214$	0.0655248	+	0.287083i	0.00447919	+	0.0196246i
$215$	−9.75000			−0.664944
$216$		0			0
$217$	−5.98090	−	2.88025i	−0.406010	−	0.195524i
$218$	0.522226	+	0.251491i	0.0353696	+	0.0170331i
$219$		0			0
$220$	−3.30953			−0.223129
$221$	1.76033	+	7.71250i	0.118413	+	0.518799i
$222$		0			0
$223$	−1.72636	+	7.56368i	−0.115606	+	0.506501i	0.883658	+	0.468133i	$0.155073\pi$
$223$	−1.72636	+	7.56368i	−0.115606	+	0.506501i	−0.999264	+	0.0383684i	$0.987784\pi$
$224$	−0.191107	+	0.837294i	−0.0127689	+	0.0559441i
$225$		0			0
$226$	0.606546	+	0.292097i	0.0403468	+	0.0194300i
$227$	−6.19669	+	2.98417i	−0.411289	+	0.198066i	−0.628075	−	0.778153i	$-0.716157\pi$
$227$	−6.19669	+	2.98417i	−0.411289	+	0.198066i	0.216786	+	0.976219i	$0.430443\pi$
$228$		0			0
$229$	11.1290	+	13.9554i	0.735427	+	0.922196i	0.999100	−	0.0424159i	$-0.0135054\pi$
$229$	11.1290	+	13.9554i	0.735427	+	0.922196i	−0.263673	+	0.964612i	$0.584934\pi$
$230$	−0.0771403	+	0.0371488i	−0.00508648	+	0.00244952i
$231$		0			0
$232$	0.846891	+	0.0653249i	0.0556011	+	0.00428879i
$233$	−11.1233			−0.728710			−0.364355	−	0.931260i	$-0.618710\pi$
$233$	−11.1233			−0.728710			−0.364355	+	0.931260i	$0.618710\pi$
$234$		0			0
$235$	25.6926	+	32.2175i	1.67600	+	2.10164i
$236$	−10.3672	+	13.0001i	−0.674848	+	0.846232i
$237$		0			0
$238$	−0.225625	−	0.108655i	−0.0146251	−	0.00704308i
$239$	2.73847	+	3.43393i	0.177137	+	0.222123i	0.862471	−	0.506106i	$-0.168915\pi$
$239$	2.73847	+	3.43393i	0.177137	+	0.222123i	−0.685334	+	0.728228i	$0.740344\pi$
$240$		0			0
$241$	−0.965005	+	4.22796i	−0.0621614	+	0.272347i	−0.996452	−	0.0841661i	$-0.973177\pi$
$241$	−0.965005	+	4.22796i	−0.0621614	+	0.272347i	0.934290	+	0.356513i	$0.116035\pi$
$242$	−0.264207	+	0.331306i	−0.0169839	+	0.0212971i
$243$		0			0
$244$	−20.2556			−1.29673
$245$	−2.68612	−	11.7687i	−0.171610	−	0.751873i
$246$		0			0
$247$	0.369265	+	0.177829i	0.0234958	+	0.0113150i
$248$	0.128291	+	0.562078i	0.00814647	+	0.0356920i
$249$		0			0
$250$	0.0181666	+	0.0795929i	0.00114895	+	0.00503390i
$251$	−11.6250	+	14.5773i	−0.733763	+	0.920110i	−0.999029	−	0.0440654i	$-0.985969\pi$
$251$	−11.6250	+	14.5773i	−0.733763	+	0.920110i	0.265265	+	0.964175i	$0.414540\pi$
$252$		0			0
$253$	−0.0752089	+	0.329512i	−0.00472834	+	0.0207162i
$254$	0.0714600	+	0.0896080i	0.00448380	+	0.00562251i
$255$		0			0
$256$	−14.3035	+	6.88819i	−0.893967	+	0.430512i
$257$	19.6769	−	24.6741i	1.22741	−	1.53913i	0.475753	−	0.879579i	$-0.342175\pi$
$257$	19.6769	−	24.6741i	1.22741	−	1.53913i	0.751661	−	0.659550i	$-0.229253\pi$
$258$		0			0
$259$	7.24347	−	3.48827i	0.450087	−	0.216751i
$260$	−14.7494			−0.914716
$261$		0			0
$262$	0.449169			0.0277498
$263$	1.85557	−	0.893596i	0.114419	−	0.0551015i	−0.375798	−	0.926701i	$-0.622632\pi$
$263$	1.85557	−	0.893596i	0.114419	−	0.0551015i	0.490218	+	0.871600i	$0.336917\pi$
$264$		0			0
$265$	−3.30890	+	4.14923i	−0.203264	+	0.254885i
$266$	−0.0116894	+	0.00562932i	−0.000716724	+	0.000345156i
$267$		0			0
$268$	−5.05879	−	6.34352i	−0.309015	−	0.387492i
$269$	4.97240	−	21.7855i	0.303173	−	1.32829i	−0.562135	−	0.827045i	$-0.690020\pi$
$269$	4.97240	−	21.7855i	0.303173	−	1.32829i	0.865308	−	0.501241i	$-0.167123\pi$
$270$		0			0
$271$	5.54826	−	6.95730i	0.337033	−	0.422626i	−0.584217	−	0.811598i	$-0.698598\pi$
$271$	5.54826	−	6.95730i	0.337033	−	0.422626i	0.921250	+	0.388972i	$0.127170\pi$
$272$	−3.10398	−	13.5994i	−0.188206	−	0.824586i
$273$		0			0
$274$	0.121735	+	0.533355i	0.00735427	+	0.0322212i
$275$	2.57803	+	1.24152i	0.155461	+	0.0748662i
$276$		0			0
$277$	−5.09383	−	22.3175i	−0.306059	−	1.34093i	−0.860815	−	0.508918i	$-0.830046\pi$
$277$	−5.09383	−	22.3175i	−0.306059	−	1.34093i	0.554756	−	0.832013i	$-0.312811\pi$
$278$	0.737230			0.0442161
$279$		0			0
$280$	0.582447	−	0.730365i	0.0348079	−	0.0436477i
$281$	1.56814	−	6.87048i	0.0935476	−	0.409859i	−0.906373	−	0.422479i	$-0.861160\pi$
$281$	1.56814	−	6.87048i	0.0935476	−	0.409859i	0.999920	+	0.0126201i	$0.00401722\pi$
$282$		0			0
$283$	4.58546	+	5.74998i	0.272577	+	0.341801i	0.899213	−	0.437511i	$-0.144140\pi$
$283$	4.58546	+	5.74998i	0.272577	+	0.341801i	−0.626636	+	0.779312i	$0.715569\pi$
$284$	24.6487	+	11.8702i	1.46263	+	0.704365i
$285$		0			0
$286$	0.0282676	−	0.0354465i	0.00167150	−	0.00209599i
$287$	6.05250	+	7.58959i	0.357268	+	0.448000i
$288$		0			0
$289$	−4.78185			−0.281285
$290$	−0.599195	−	0.347691i	−0.0351859	−	0.0204171i
$291$		0			0
$292$	6.29565	−	3.03183i	0.368425	−	0.177424i
$293$	−10.2778	−	12.8880i	−0.600438	−	0.752925i	0.385008	−	0.922913i	$-0.374199\pi$
$293$	−10.2778	−	12.8880i	−0.600438	−	0.752925i	−0.985446	+	0.169988i	$0.945627\pi$
$294$		0			0
$295$	24.4462	−	11.7727i	1.42331	−	0.685431i
$296$	−0.629092	−	0.302955i	−0.0365652	−	0.0176089i
$297$		0			0
$298$	0.0770219	−	0.337455i	0.00446176	−	0.0195482i
$299$	−0.335178	+	1.46851i	−0.0193838	+	0.0849262i
$300$		0			0
$301$	−1.20827	−	5.29377i	−0.0696434	−	0.305128i
$302$	0.862237			0.0496162
$303$		0			0
$304$	−0.651123	−	0.313564i	−0.0373445	−	0.0179841i
$305$	29.7799	+	14.3413i	1.70519	+	0.821178i
$306$		0			0
$307$	−17.7386			−1.01239			−0.506197	−	0.862418i	$-0.668949\pi$
$307$	−17.7386			−1.01239			−0.506197	+	0.862418i	$0.668949\pi$
$308$	−0.410134	−	1.79691i	−0.0233696	−	0.102389i
$309$		0			0
$310$	0.104632	−	0.458423i	0.00594271	−	0.0260367i
$311$	3.03536	−	13.2988i	0.172120	−	0.754105i	−0.813004	−	0.582258i	$-0.802169\pi$
$311$	3.03536	−	13.2988i	0.172120	−	0.754105i	0.985124	−	0.171847i	$-0.0549735\pi$
$312$		0			0
$313$	−12.4014	−	5.97221i	−0.700970	−	0.337570i	0.0492232	−	0.998788i	$-0.484325\pi$
$313$	−12.4014	−	5.97221i	−0.700970	−	0.337570i	−0.750194	+	0.661218i	$0.770040\pi$
$314$	0.424010	−	0.204192i	0.0239282	−	0.0115232i
$315$		0			0
$316$	−15.2984	−	19.1835i	−0.860600	−	1.07916i
$317$	5.14252	−	2.47651i	0.288833	−	0.139095i	−0.283857	−	0.958867i	$-0.591614\pi$
$317$	5.14252	−	2.47651i	0.288833	−	0.139095i	0.572690	+	0.819772i	$0.305900\pi$
$318$		0			0
$319$	−2.54785	+	0.993547i	−0.142652	+	0.0556279i
$320$	25.9669			1.45159
$321$		0			0
$322$	−0.0297296	−	0.0372797i	−0.00165676	−	0.00207752i
$323$	0.394675	−	0.494907i	0.0219603	−	0.0275374i
$324$		0			0
$325$	11.4893	+	5.53297i	0.637313	+	0.306914i
$326$	0.208182	+	0.261052i	0.0115301	+	0.0144583i
$327$		0			0
$328$	0.187605	−	0.821950i	0.0103587	−	0.0453846i
$329$	−14.3085	+	17.9424i	−0.788856	+	0.989194i
$330$		0			0
$331$	−1.89612			−0.104220			−0.0521100	−	0.998641i	$-0.516595\pi$
$331$	−1.89612			−0.104220			−0.0521100	+	0.998641i	$0.516595\pi$
$332$	−1.17434	−	5.14512i	−0.0644502	−	0.282375i
$333$		0			0
$334$	0.261412	+	0.125889i	0.0143038	+	0.00688835i
$335$	2.94617	+	12.9080i	0.160966	+	0.705239i
$336$		0			0
$337$	3.16304	+	13.8582i	0.172302	+	0.754902i	0.985047	+	0.172284i	$0.0551146\pi$
$337$	3.16304	+	13.8582i	0.172302	+	0.754902i	−0.812746	+	0.582618i	$0.802028\pi$
$338$	−0.193763	+	0.242971i	−0.0105393	+	0.0132159i
$339$		0			0
$340$	−5.06905	+	22.2090i	−0.274908	+	1.20445i
$341$	−1.15731	−	1.45122i	−0.0626720	−	0.0785882i
$342$		0			0
$343$	17.5109	−	8.43282i	0.945501	−	0.455329i
$344$	−0.294029	+	0.368700i	−0.0158530	+	0.0198790i
$345$		0			0
$346$	−0.842899	+	0.405919i	−0.0453145	+	0.0218223i
$347$	27.0820			1.45384			0.726918	−	0.686724i	$-0.240952\pi$
$347$	27.0820			1.45384			0.726918	+	0.686724i	$0.240952\pi$
$348$		0			0
$349$	−6.40948			−0.343092			−0.171546	−	0.985176i	$-0.554876\pi$
$349$	−6.40948			−0.343092			−0.171546	+	0.985176i	$0.554876\pi$
$350$	−0.363705	+	0.175151i	−0.0194409	+	0.00936223i
$351$		0			0
$352$	−0.149727	+	0.187752i	−0.00798047	+	0.0100072i
$353$	6.84796	−	3.29780i	0.364480	−	0.175524i	−0.242675	−	0.970108i	$-0.578025\pi$
$353$	6.84796	−	3.29780i	0.364480	−	0.175524i	0.607155	+	0.794583i	$0.292311\pi$
$354$		0			0
$355$	−27.8344	−	34.9032i	−1.47730	−	1.85247i
$356$	−4.82912	+	21.1578i	−0.255943	+	1.12136i
$357$		0			0
$358$	−0.589350	+	0.739022i	−0.0311481	+	0.0390585i
$359$	7.01722	+	30.7445i	0.370355	+	1.62263i	0.725781	+	0.687926i	$0.241479\pi$
$359$	7.01722	+	30.7445i	0.370355	+	1.62263i	−0.355426	+	0.934704i	$0.615664\pi$
$360$		0			0
$361$	4.22060	+	18.4917i	0.222137	+	0.973245i
$362$	0.662571	+	0.319078i	0.0348240	+	0.0167703i
$363$		0			0
$364$	−1.82781	−	8.00818i	−0.0958035	−	0.419743i
$365$	−11.4025			−0.596834
$366$		0			0
$367$	−7.45437	+	9.34748i	−0.389115	+	0.487934i	−0.937350	−	0.348390i	$-0.886729\pi$
$367$	−7.45437	+	9.34748i	−0.389115	+	0.487934i	0.548235	+	0.836324i	$0.315300\pi$
$368$	0.591018	−	2.58942i	0.0308089	−	0.134983i
$369$		0			0
$370$	0.355062	+	0.445233i	0.0184588	+	0.0231466i
$371$	−2.66289	−	1.28238i	−0.138250	−	0.0665778i
$372$		0			0
$373$	18.2660	−	22.9049i	0.945778	−	1.18597i	−0.0366500	−	0.999328i	$-0.511669\pi$
$373$	18.2660	−	22.9049i	0.945778	−	1.18597i	0.982428	−	0.186640i	$-0.0597599\pi$
$374$	−0.0436588	−	0.0547464i	−0.00225754	−	0.00283087i
$375$		0			0
$376$	1.99312			0.102787
$377$	−11.3548	+	4.42787i	−0.584804	+	0.228047i
$378$		0			0
$379$	20.4464	−	9.84645i	1.05026	−	0.505778i	0.172564	−	0.984998i	$-0.444795\pi$
$379$	20.4464	−	9.84645i	1.05026	−	0.505778i	0.877695	+	0.479220i	$0.159080\pi$
$380$	0.735852	+	0.922729i	0.0377484	+	0.0473350i
$381$		0			0
$382$	0.748305	−	0.360365i	0.0382866	−	0.0184379i
$383$	−3.32145	−	1.59953i	−0.169718	−	0.0817320i	0.347096	−	0.937830i	$-0.387168\pi$
$383$	−3.32145	−	1.59953i	−0.169718	−	0.0817320i	−0.516814	+	0.856098i	$0.672882\pi$
$384$		0			0
$385$	−0.669260	+	2.93222i	−0.0341087	+	0.149440i
$386$	0.114868	−	0.503268i	0.00584661	−	0.0256157i
$387$		0			0
$388$	−3.48279	−	15.2591i	−0.176812	−	0.774664i
$389$	13.9852			0.709080			0.354540	−	0.935041i	$-0.384637\pi$
$389$	13.9852			0.709080			0.354540	+	0.935041i	$0.384637\pi$
$390$		0			0
$391$	2.09603	+	1.00939i	0.106001	+	0.0510472i
$392$	−0.526042	−	0.253329i	−0.0265691	−	0.0127950i
$393$		0			0
$394$	−0.524416			−0.0264197
$395$	8.90955	+	39.0353i	0.448288	+	1.96408i
$396$		0			0
$397$	−0.387060	+	1.69582i	−0.0194260	+	0.0851108i	−0.983712	−	0.179753i	$-0.942470\pi$
$397$	−0.387060	+	1.69582i	−0.0194260	+	0.0851108i	0.964286	+	0.264864i	$0.0853272\pi$
$398$	0.0113029	−	0.0495214i	0.000566565	−	0.00248228i
$399$		0			0
$400$	−20.2591	−	9.75626i	−1.01295	−	0.487813i
$401$	−2.36625	+	1.13953i	−0.118165	+	0.0569052i	−0.492032	−	0.870577i	$-0.663746\pi$
$401$	−2.36625	+	1.13953i	−0.118165	+	0.0569052i	0.373867	+	0.927482i	$0.378032\pi$
$402$		0			0
$403$	−5.15771	−	6.46756i	−0.256924	−	0.322172i
$404$	11.6528	−	5.61169i	0.579748	−	0.279192i
$405$		0			0
$406$	0.114524	−	0.368421i	0.00568373	−	0.0182844i
$407$	2.24803			0.111431
$408$		0			0
$409$	16.5003	+	20.6908i	0.815889	+	1.02309i	0.999198	+	0.0400373i	$0.0127477\pi$
$409$	16.5003	+	20.6908i	0.815889	+	1.02309i	−0.183309	+	0.983055i	$0.558681\pi$
$410$	−0.428719	+	0.537596i	−0.0211729	+	0.0265500i
$411$		0			0
$412$	8.81807	+	4.24656i	0.434435	+	0.209213i
$413$	9.42148	+	11.8142i	0.463601	+	0.581337i
$414$		0			0
$415$	−1.91630	+	8.39584i	−0.0940673	+	0.412136i
$416$	−0.667277	+	0.836738i	−0.0327159	+	0.0410245i
$417$		0			0
$418$	−0.00362784			−0.000177443
$419$	6.07020	+	26.5953i	0.296549	+	1.29926i	0.875228	+	0.483710i	$0.160711\pi$
$419$	6.07020	+	26.5953i	0.296549	+	1.29926i	−0.578680	+	0.815555i	$0.696432\pi$
$420$		0			0
$421$	−8.90770	−	4.28972i	−0.434135	−	0.209068i	0.204036	−	0.978963i	$-0.434594\pi$
$421$	−8.90770	−	4.28972i	−0.434135	−	0.209068i	−0.638170	+	0.769895i	$0.720308\pi$
$422$	−0.0898441	−	0.393633i	−0.00437354	−	0.0191617i
$423$		0			0
$424$	0.0571191	+	0.250255i	0.00277395	+	0.0121535i
$425$	12.2800	−	15.3986i	0.595665	−	0.746941i
$426$		0			0
$427$	−4.09612	+	17.9463i	−0.198225	+	0.868482i
$428$	9.30102	+	11.6631i	0.449582	+	0.563758i
$429$		0			0
$430$	0.346529	−	0.166880i	0.0167111	−	0.00804766i
$431$	−22.6155	+	28.3590i	−1.08935	+	1.36600i	−0.164190	+	0.986429i	$0.552501\pi$
$431$	−22.6155	+	28.3590i	−1.08935	+	1.36600i	−0.925161	+	0.379574i	$0.876070\pi$
$432$		0			0
$433$	−32.6318	+	15.7146i	−1.56818	+	0.755197i	−0.997807	−	0.0661865i	$-0.978917\pi$
$433$	−32.6318	+	15.7146i	−1.56818	+	0.755197i	−0.570376	+	0.821384i	$0.693202\pi$
$434$	0.261868			0.0125701
$435$		0			0
$436$	29.3640			1.40628
$437$	0.108593	−	0.0522957i	0.00519471	−	0.00250164i
$438$		0			0
$439$	−14.9426	+	18.7374i	−0.713172	+	0.894289i	−0.997930	−	0.0643102i	$-0.979515\pi$
$439$	−14.9426	+	18.7374i	−0.713172	+	0.894289i	0.284758	+	0.958599i	$0.408087\pi$
$440$	0.235343	−	0.113335i	0.0112195	−	0.00540305i
$441$		0			0
$442$	−0.194571	−	0.243984i	−0.00925480	−	0.0116051i
$443$	1.27786	−	5.59868i	0.0607131	−	0.266001i	−0.935457	−	0.353441i	$-0.885011\pi$
$443$	1.27786	−	5.59868i	0.0607131	−	0.266001i	0.996170	+	0.0874399i	$0.0278686\pi$
$444$		0			0
$445$	22.0798	−	27.6872i	1.04668	−	1.31250i
$446$	−0.0681016	−	0.298373i	−0.00322470	−	0.0141284i
$447$		0			0
$448$	3.21795	+	14.0988i	0.152034	+	0.666103i
$449$	−1.34769	−	0.649013i	−0.0636014	−	0.0306288i	0.401813	−	0.915722i	$-0.368380\pi$
$449$	−1.34769	−	0.649013i	−0.0636014	−	0.0306288i	−0.465414	+	0.885093i	$0.654095\pi$
$450$		0			0
$451$	0.604006	+	2.64632i	0.0284415	+	0.124610i
$452$	34.1052			1.60417
$453$		0			0
$454$	0.169163	−	0.212124i	0.00793921	−	0.00995545i
$455$	−2.98264	+	13.0678i	−0.139828	+	0.612628i
$456$		0			0
$457$	16.8493	+	21.1283i	0.788176	+	0.988342i	0.999939	+	0.0110206i	$0.00350805\pi$
$457$	16.8493	+	21.1283i	0.788176	+	0.988342i	−0.211763	+	0.977321i	$0.567921\pi$
$458$	−0.634401	−	0.305511i	−0.0296436	−	0.0142756i
$459$		0			0
$460$	−2.70437	+	3.39118i	−0.126092	+	0.158114i
$461$	−9.68529	−	12.1450i	−0.451089	−	0.565648i	0.503339	−	0.864089i	$-0.332105\pi$
$461$	−9.68529	−	12.1450i	−0.451089	−	0.565648i	−0.954428	+	0.298441i	$0.903533\pi$
$462$		0			0
$463$	6.85055			0.318372			0.159186	−	0.987249i	$-0.449113\pi$
$463$	6.85055			0.318372			0.159186	+	0.987249i	$0.449113\pi$
$464$	20.0219	−	7.80764i	0.929495	−	0.362461i
$465$		0			0
$466$	0.395338	−	0.190385i	0.0183137	−	0.00881940i
$467$	23.1038	+	28.9713i	1.06912	+	1.34063i	0.936973	+	0.349402i	$0.113615\pi$
$467$	23.1038	+	28.9713i	1.06912	+	1.34063i	0.132145	+	0.991230i	$0.457813\pi$
$468$		0			0
$469$	−6.64331	+	3.19925i	−0.306759	+	0.147728i
$470$	−1.46458	−	0.705306i	−0.0675561	−	0.0325333i
$471$		0			0
$472$	0.292030	−	1.27947i	0.0134418	−	0.0588923i
$473$	0.337853	−	1.48023i	0.0155345	−	0.0680611i
$474$		0			0
$475$	−0.227062	−	0.994822i	−0.0104183	−	0.0456455i
$476$	−12.6866			−0.581487
$477$		0			0
$478$	−0.156104	−	0.0751758i	−0.00714004	−	0.00343846i
$479$	−24.7741	−	11.9306i	−1.13196	−	0.545122i	−0.228391	−	0.973570i	$-0.573346\pi$
$479$	−24.7741	−	11.9306i	−1.13196	−	0.545122i	−0.903567	+	0.428447i	$0.859061\pi$
$480$		0			0
$481$	10.0186			0.456810
$482$	−0.0380676	−	0.166785i	−0.00173393	−	0.00759685i
$483$		0			0
$484$	−4.77697	+	20.9293i	−0.217135	+	0.951331i
$485$	−5.68325	+	24.8999i	−0.258063	+	1.13065i
$486$		0			0
$487$	5.72112	+	2.75514i	0.259249	+	0.124848i	0.558994	−	0.829172i	$-0.311187\pi$
$487$	5.72112	+	2.75514i	0.259249	+	0.124848i	−0.299745	+	0.954019i	$0.596902\pi$
$488$	1.44039	−	0.693654i	0.0652033	−	0.0314003i
$489$		0			0
$490$	0.296900	+	0.372301i	0.0134126	+	0.0168188i
$491$	−30.1094	+	14.4999i	−1.35882	+	0.654373i	−0.964373	−	0.264546i	$-0.914778\pi$
$491$	−30.1094	+	14.4999i	−1.35882	+	0.654373i	−0.394446	+	0.918919i	$0.629064\pi$
$492$		0			0
$493$	2.76487	+	18.6194i	0.124524	+	0.838575i
$494$	−0.0161679			−0.000727429
$495$		0			0
$496$	9.09457	+	11.4042i	0.408358	+	0.512065i
$497$	15.5014	−	19.4381i	0.695331	−	0.871918i
$498$		0			0
$499$	−2.61809	−	1.26081i	−0.117202	−	0.0564414i	0.374364	−	0.927282i	$-0.377861\pi$
$499$	−2.61809	−	1.26081i	−0.117202	−	0.0564414i	−0.491566	+	0.870840i	$0.663575\pi$
$500$	2.57868	+	3.23356i	0.115322	+	0.144609i
$501$		0			0
$502$	0.163667	−	0.717070i	0.00730480	−	0.0320044i
$503$	15.8508	−	19.8763i	0.706752	−	0.886239i	−0.290755	−	0.956797i	$-0.593907\pi$
$503$	15.8508	−	19.8763i	0.706752	−	0.886239i	0.997508	+	0.0705581i	$0.0224780\pi$
$504$		0			0
$505$	−21.1052			−0.939169
$506$	−0.00296685	−	0.0129986i	−0.000131892	−	0.000577858i
$507$		0			0
$508$	5.23130	+	2.51926i	0.232101	+	0.111774i
$509$	−0.298764	−	1.30897i	−0.0132425	−	0.0580192i	0.967875	−	0.251432i	$-0.0809015\pi$
$509$	−0.298764	−	1.30897i	−0.0132425	−	0.0580192i	−0.981117	+	0.193413i	$0.938044\pi$
$510$		0			0
$511$	−1.41305	−	6.19100i	−0.0625099	−	0.273874i
$512$	1.96152	−	2.45967i	0.0866877	−	0.108703i
$513$		0			0
$514$	−0.277029	+	1.21374i	−0.0122192	+	0.0535359i
$515$	−9.95777	−	12.4867i	−0.438792	−	0.550228i
$516$		0			0
$517$	−5.78150	+	2.78423i	−0.254270	+	0.122450i
$518$	−0.197739	+	0.247957i	−0.00868815	+	0.0108946i
$519$		0			0
$520$	1.04884	−	0.505093i	0.0459945	−	0.0221498i
$521$	−4.68838			−0.205402			−0.102701	−	0.994712i	$-0.532748\pi$
$521$	−4.68838			−0.205402			−0.102701	+	0.994712i	$0.532748\pi$
$522$		0			0
$523$	28.1658			1.23160			0.615802	−	0.787901i	$-0.288832\pi$
$523$	28.1658			1.23160			0.615802	+	0.787901i	$0.288832\pi$
$524$	20.5015	−	9.87301i	0.895613	−	0.431304i
$525$		0			0
$526$	−0.0506551	+	0.0635195i	−0.00220867	+	0.00276958i
$527$	−11.5112	+	5.54349i	−0.501435	+	0.241478i
$528$		0			0
$529$	−14.0641	−	17.6358i	−0.611482	−	0.766774i
$530$	0.0465856	−	0.204105i	0.00202355	−	0.00886574i
$531$		0			0
$532$	−0.409806	+	0.513881i	−0.0177673	+	0.0222795i
$533$	2.69183	+	11.7937i	0.116596	+	0.510840i
$534$		0			0
$535$	−5.41678	−	23.7325i	−0.234188	−	1.02604i
$536$	0.576969	+	0.277853i	0.0249212	+	0.0120014i
$537$		0			0
$538$	0.196152	+	0.859397i	0.00845670	+	0.0370512i
$539$	1.87978			0.0809680
$540$		0			0
$541$	3.66224	−	4.59230i	0.157452	−	0.197438i	−0.696848	−	0.717219i	$-0.745415\pi$
$541$	3.66224	−	4.59230i	0.157452	−	0.197438i	0.854300	+	0.519780i	$0.173986\pi$
$542$	−0.0781132	+	0.342236i	−0.00335525	+	0.0147003i
$543$		0			0
$544$	1.03060	+	1.29233i	0.0441864	+	0.0554081i
$545$	−43.1712	−	20.7901i	−1.84925	−	0.890552i
$546$		0			0
$547$	21.1523	−	26.5242i	0.904409	−	1.13409i	−0.0860510	−	0.996291i	$-0.527425\pi$
$547$	21.1523	−	26.5242i	0.904409	−	1.13409i	0.990460	−	0.137802i	$-0.0440038\pi$
$548$	17.2798	+	21.6682i	0.738158	+	0.925621i
$549$		0			0
$550$	−0.112877			−0.00481308
$551$	0.843508	+	0.489457i	0.0359346	+	0.0208516i
$552$		0			0
$553$	−20.0901	+	9.67490i	−0.854319	+	0.411418i
$554$	0.563027	+	0.706013i	0.0239207	+	0.0299956i
$555$		0			0
$556$	33.6495	−	16.2048i	1.42706	−	0.687235i
$557$	29.4888	+	14.2011i	1.24948	+	0.601719i	0.937373	−	0.348327i	$-0.113250\pi$
$557$	29.4888	+	14.2011i	1.24948	+	0.601719i	0.312109	+	0.950046i	$0.398964\pi$
$558$		0			0
$559$	1.50569	−	6.59684i	0.0636837	−	0.279017i
$560$	5.25928	−	23.0424i	0.222245	−	0.973720i
$561$		0			0
$562$	0.0618602	+	0.271027i	0.00260942	+	0.0114326i
$563$	18.8319			0.793669			0.396834	−	0.917890i	$-0.370109\pi$
$563$	18.8319			0.793669			0.396834	+	0.917890i	$0.370109\pi$
$564$		0			0
$565$	−50.1417	−	24.1470i	−2.10948	−	1.01587i
$566$	−0.261390	−	0.125879i	−0.0109870	−	0.00529108i
$567$		0			0
$568$	−2.15928			−0.0906013
$569$	−5.43036	−	23.7920i	−0.227653	−	0.997411i	−0.951548	−	0.307501i	$-0.900507\pi$
$569$	−5.43036	−	23.7920i	−0.227653	−	0.997411i	0.723895	−	0.689910i	$-0.242350\pi$
$570$		0			0
$571$	−2.71722	+	11.9049i	−0.113712	+	0.498205i	0.885711	+	0.464237i	$0.153671\pi$
$571$	−2.71722	+	11.9049i	−0.113712	+	0.498205i	−0.999423	+	0.0339675i	$0.989186\pi$
$572$	0.511089	−	2.23923i	0.0213697	−	0.0936269i
$573$		0			0
$574$	−0.345017	−	0.166152i	−0.0144007	−	0.00693504i
$575$	3.37877	−	1.62713i	0.140905	−	0.0678561i
$576$		0			0
$577$	−20.4328	−	25.6219i	−0.850627	−	1.06665i	−0.996998	−	0.0774226i	$-0.975331\pi$
$577$	−20.4328	−	25.6219i	−0.850627	−	1.06665i	0.146372	−	0.989230i	$-0.453240\pi$
$578$	0.169954	−	0.0818455i	0.00706915	−	0.00340432i
$579$		0			0
$580$	−34.9916	−	2.69907i	−1.45295	−	0.112073i
$581$	−4.79601			−0.198972
$582$		0			0
$583$	−0.515273	−	0.646131i	−0.0213404	−	0.0267600i
$584$	−0.343863	+	0.431190i	−0.0142291	+	0.0178428i
$585$		0			0
$586$	0.585879	+	0.282145i	0.0242025	+	0.0116553i
$587$	−19.4380	−	24.3744i	−0.802291	−	1.00604i	−0.999669	−	0.0257137i	$-0.991814\pi$
$587$	−19.4380	−	24.3744i	−0.802291	−	1.00604i	0.197378	−	0.980327i	$-0.436757\pi$
$588$		0			0
$589$	−0.147294	+	0.645339i	−0.00606916	+	0.0265907i
$590$	−0.667355	+	0.836836i	−0.0274746	+	0.0344520i
$591$		0			0
$592$	−17.6658			−0.726059
$593$	−6.99611	−	30.6519i	−0.287296	−	1.25872i	−0.888220	−	0.459418i	$-0.848058\pi$
$593$	−6.99611	−	30.6519i	−0.287296	−	1.25872i	0.600924	−	0.799306i	$-0.294799\pi$
$594$		0			0
$595$	18.6519	+	8.98227i	0.764653	+	0.368237i
$596$	−3.90194	−	17.0955i	−0.159830	−	0.700259i
$597$		0			0
$598$	−0.0132221	−	0.0579299i	−0.000540693	−	0.00236893i
$599$	2.23694	−	2.80504i	0.0913990	−	0.114611i	−0.734029	−	0.679118i	$-0.762362\pi$
$599$	2.23694	−	2.80504i	0.0913990	−	0.114611i	0.825428	+	0.564507i	$0.190934\pi$
$600$		0			0
$601$	−7.67834	+	33.6410i	−0.313206	+	1.37225i	0.536015	+	0.844208i	$0.319929\pi$
$601$	−7.67834	+	33.6410i	−0.313206	+	1.37225i	−0.849221	+	0.528037i	$0.822928\pi$
$602$	0.133551	+	0.167468i	0.00544314	+	0.00682548i
$603$		0			0
$604$	39.3552	−	18.9525i	1.60134	−	0.771165i
$605$	21.8414	−	27.3882i	0.887978	−	1.11349i
$606$		0			0
$607$	15.5482	−	7.48761i	0.631082	−	0.303913i	−0.0908634	−	0.995863i	$-0.528963\pi$
$607$	15.5482	−	7.48761i	0.631082	−	0.303913i	0.721945	+	0.691950i	$0.243248\pi$
$608$	0.0856376			0.00347306
$609$		0			0
$610$	−1.30389			−0.0527928
$611$	−25.7660	+	12.4083i	−1.04238	+	0.501984i
$612$		0			0
$613$	−14.6921	+	18.4233i	−0.593407	+	0.744108i	−0.984334	−	0.176313i	$-0.943583\pi$
$613$	−14.6921	+	18.4233i	−0.593407	+	0.744108i	0.390927	+	0.920422i	$0.372154\pi$
$614$	0.630456	−	0.303612i	0.0254431	−	0.0122528i
$615$		0			0
$616$	0.0907004	+	0.113735i	0.00365442	+	0.00458250i
$617$	−3.54391	+	15.5269i	−0.142672	+	0.625088i	0.852136	+	0.523320i	$0.175307\pi$
$617$	−3.54391	+	15.5269i	−0.142672	+	0.625088i	−0.994808	+	0.101768i	$0.967550\pi$
$618$		0			0
$619$	25.4609	−	31.9270i	1.02336	−	1.28325i	0.0649412	−	0.997889i	$-0.479314\pi$
$619$	25.4609	−	31.9270i	1.02336	−	1.28325i	0.958419	−	0.285364i	$-0.0921146\pi$
$620$	−5.30068	−	23.2238i	−0.212880	−	0.932689i
$621$		0			0
$622$	0.119739	+	0.524612i	0.00480110	+	0.0210350i
$623$	17.7690	+	8.55712i	0.711902	+	0.342834i
$624$		0			0
$625$	4.76732	+	20.8870i	0.190693	+	0.835480i
$626$	0.542985			0.0217020
$627$		0			0
$628$	14.8649	−	18.6400i	0.593173	−	0.743816i
$629$	3.44319	−	15.0856i	0.137289	−	0.601503i
$630$		0			0
$631$	−12.1350	−	15.2169i	−0.483088	−	0.605774i	0.479233	−	0.877688i	$-0.340915\pi$
$631$	−12.1350	−	15.2169i	−0.483088	−	0.605774i	−0.962322	+	0.271914i	$0.912343\pi$
$632$	1.74482	+	0.840261i	0.0694052	+	0.0334238i
$633$		0			0
$634$	−0.140385	+	0.176038i	−0.00557541	+	0.00699135i
$635$	−5.90742	−	7.40768i	−0.234429	−	0.293965i
$636$		0			0
$637$	8.37749			0.331928
$638$	0.0735491	−	0.0789209i	0.00291184	−	0.00312451i
$639$		0			0
$640$	−3.70170	+	1.78265i	−0.146323	+	0.0704653i
$641$	−25.0201	−	31.3742i	−0.988233	−	1.23920i	−0.970932	−	0.239355i	$-0.923064\pi$
$641$	−25.0201	−	31.3742i	−0.988233	−	1.23920i	−0.0173008	−	0.999850i	$-0.505507\pi$
$642$		0			0
$643$	−17.5493	+	8.45132i	−0.692078	+	0.333287i	−0.746645	−	0.665223i	$-0.768337\pi$
$643$	−17.5493	+	8.45132i	−0.692078	+	0.333287i	0.0545666	+	0.998510i	$0.482622\pi$
$644$	−2.17638	−	1.04809i	−0.0857615	−	0.0413006i
$645$		0			0
$646$	−0.00555658	+	0.0243450i	−0.000218621	+	0.000957840i
$647$	−6.78166	+	29.7124i	−0.266615	+	1.16812i	0.647308	+	0.762228i	$0.275895\pi$
$647$	−6.78166	+	29.7124i	−0.266615	+	1.16812i	−0.913923	+	0.405887i	$0.866963\pi$
$648$		0			0
$649$	0.940211	+	4.11933i	0.0369065	+	0.161698i
$650$	−0.503049			−0.0197312
$651$		0			0
$652$	15.2402	+	7.33928i	0.596851	+	0.287428i
$653$	−38.5788	−	18.5786i	−1.50971	−	0.727036i	−0.517977	−	0.855394i	$-0.673315\pi$
$653$	−38.5788	−	18.5786i	−1.50971	−	0.727036i	−0.991728	+	0.128359i	$0.959029\pi$
$654$		0			0
$655$	−37.1317			−1.45086
$656$	−4.74649	−	20.7957i	−0.185319	−	0.811937i
$657$		0			0
$658$	0.201448	−	0.882601i	0.00785326	−	0.0344074i
$659$	−4.50470	+	19.7364i	−0.175478	+	0.768820i	0.808204	+	0.588903i	$0.200440\pi$
$659$	−4.50470	+	19.7364i	−0.175478	+	0.768820i	−0.983682	+	0.179917i	$0.942417\pi$
$660$		0			0
$661$	−40.2615	−	19.3889i	−1.56599	−	0.754142i	−0.568351	−	0.822786i	$-0.692418\pi$
$661$	−40.2615	−	19.3889i	−1.56599	−	0.754142i	−0.997641	+	0.0686443i	$0.978133\pi$
$662$	0.0673909	−	0.0324537i	0.00261922	−	0.00126135i
$663$		0			0
$664$	0.259703	+	0.325657i	0.0100784	+	0.0126380i
$665$	0.966335	−	0.465363i	0.0374729	−	0.0180460i
$666$		0			0
$667$	−1.06391	+	3.42258i	−0.0411949	+	0.132523i
$668$	14.6988			0.568713
$669$		0			0
$670$	−0.325643	−	0.408343i	−0.0125807	−	0.0157757i
$671$	−3.20920	+	4.02420i	−0.123890	+	0.155353i
$672$		0			0
$673$	28.2795	+	13.6187i	1.09010	+	0.524963i	0.890531	−	0.454922i	$-0.150333\pi$
$673$	28.2795	+	13.6187i	1.09010	+	0.524963i	0.199565	+	0.979885i	$0.436047\pi$
$674$	−0.349614	−	0.438402i	−0.0134666	−	0.0168866i
$675$		0			0
$676$	−3.50331	+	15.3490i	−0.134743	+	0.590346i
$677$	6.69919	−	8.40052i	0.257471	−	0.322858i	−0.636249	−	0.771484i	$-0.719515\pi$
$677$	6.69919	−	8.40052i	0.257471	−	0.322858i	0.893720	+	0.448625i	$0.148086\pi$
$678$		0			0
$679$	−14.2237			−0.545857
$680$	−0.400084	−	1.75288i	−0.0153425	−	0.0672200i
$681$		0			0
$682$	0.0659716	+	0.0317702i	0.00252618	+	0.00121655i
$683$	−1.03313	−	4.52645i	−0.0395317	−	0.173200i	0.951308	−	0.308241i	$-0.0997404\pi$
$683$	−1.03313	−	4.52645i	−0.0395317	−	0.173200i	−0.990840	+	0.135041i	$0.956883\pi$
$684$		0			0
$685$	−10.0635	−	44.0912i	−0.384508	−	1.68464i
$686$	−0.478029	+	0.599430i	−0.0182512	+	0.0228863i
$687$		0			0
$688$	−2.65497	+	11.6322i	−0.101220	+	0.443473i
$689$	−2.29638	−	2.87957i	−0.0874850	−	0.109703i
$690$		0			0
$691$	33.8748	−	16.3133i	1.28866	−	0.620586i	0.341059	−	0.940042i	$-0.389214\pi$
$691$	33.8748	−	16.3133i	1.28866	−	0.620586i	0.947601	+	0.319456i	$0.103500\pi$
$692$	−29.5502	+	37.0548i	−1.12333	+	1.40861i
$693$		0			0
$694$	−0.962533	+	0.463532i	−0.0365373	+	0.0175954i
$695$	−60.9450			−2.31178
$696$		0			0
$697$	18.6835			0.707689
$698$	0.227802	−	0.109704i	0.00862245	−	0.00415235i
$699$		0			0
$700$	−12.7507	+	15.9889i	−0.481932	+	0.604324i
$701$	−22.7922	+	10.9761i	−0.860850	+	0.414563i	−0.811593	−	0.584223i	$-0.801399\pi$
$701$	−22.7922	+	10.9761i	−0.860850	+	0.414563i	−0.0492565	+	0.998786i	$0.515685\pi$
$702$		0			0
$703$	−0.499833	−	0.626771i	−0.0188516	−	0.0236391i
$704$	−0.899796	+	3.94226i	−0.0339123	+	0.148580i
$705$		0			0
$706$	−0.186942	+	0.234418i	−0.00703565	+	0.00882242i
$707$	−2.61546	−	11.4591i	−0.0983646	−	0.430963i
$708$		0			0
$709$	−0.889239	−	3.89601i	−0.0333961	−	0.146318i	0.955481	−	0.295052i	$-0.0953371\pi$
$709$	−0.889239	−	3.89601i	−0.0333961	−	0.146318i	−0.988877	+	0.148735i	$0.952480\pi$
$710$	1.58668	+	0.764103i	0.0595469	+	0.0286763i
$711$		0			0
$712$	−0.381147	−	1.66992i	−0.0142841	−	0.0625827i
$713$	−2.43272			−0.0911060
$714$		0			0
$715$	−2.33682	+	2.93027i	−0.0873919	+	0.109586i
$716$	−10.6557	+	46.6856i	−0.398221	+	1.74472i
$717$		0			0
$718$	−0.775621	−	0.972598i	−0.0289459	−	0.0362970i
$719$	−28.9446	−	13.9390i	−1.07945	−	0.519837i	−0.192310	−	0.981334i	$-0.561598\pi$
$719$	−28.9446	−	13.9390i	−1.07945	−	0.519837i	−0.887141	+	0.461498i	$0.847312\pi$
$720$		0			0
$721$	5.54562	−	6.95399i	0.206530	−	0.258980i
$722$	−0.466507	−	0.584982i	−0.0173616	−	0.0217708i
$723$		0			0
$724$	37.2554			1.38459
$725$	26.2450	+	15.2290i	0.974713	+	0.565591i
$726$		0			0
$727$	13.4572	−	6.48065i	0.499100	−	0.240354i	−0.167358	−	0.985896i	$-0.553524\pi$
$727$	13.4572	−	6.48065i	0.499100	−	0.240354i	0.666458	+	0.745542i	$0.267809\pi$
$728$	0.404218	+	0.506873i	0.0149813	+	0.0187860i
$729$		0			0
$730$	0.405262	−	0.195164i	0.0149994	−	0.00722334i
$731$	−9.41577	−	4.53440i	−0.348255	−	0.167711i
$732$		0			0
$733$	−7.60884	+	33.3365i	−0.281039	+	1.23131i	0.615425	+	0.788195i	$0.288984\pi$
$733$	−7.60884	+	33.3365i	−0.281039	+	1.23131i	−0.896464	+	0.443116i	$0.853873\pi$
$734$	0.104949	−	0.459811i	0.00387374	−	0.0169719i
$735$		0			0
$736$	0.0700344	+	0.306841i	0.00258150	+	0.0113103i
$737$	−2.06177			−0.0759461
$738$		0			0
$739$	−23.5997	−	11.3650i	−0.868127	−	0.418068i	−0.0538534	−	0.998549i	$-0.517150\pi$
$739$	−23.5997	−	11.3650i	−0.868127	−	0.418068i	−0.814274	+	0.580481i	$0.802865\pi$
$740$	25.9926	+	12.5174i	0.955509	+	0.460149i
$741$		0			0
$742$	0.116592			0.00428023
$743$	−5.98118	−	26.2052i	−0.219428	−	0.961377i	−0.957902	−	0.287095i	$-0.907310\pi$
$743$	−5.98118	−	26.2052i	−0.219428	−	0.961377i	0.738474	−	0.674282i	$-0.235547\pi$
$744$		0			0
$745$	−6.36721	+	27.8966i	−0.233277	+	1.02205i
$746$	−0.257165	+	1.12671i	−0.00941546	+	0.0412518i
$747$		0			0
$748$	−3.19609	−	1.53915i	−0.116860	−	0.0562770i
$749$	12.2143	−	5.88209i	0.446300	−	0.214927i
$750$		0			0
$751$	20.7956	+	26.0769i	0.758843	+	0.951559i	0.999820	−	0.0189721i	$-0.00603938\pi$
$751$	20.7956	+	26.0769i	0.758843	+	0.951559i	−0.240977	+	0.970531i	$0.577468\pi$
$752$	45.4331	−	21.8794i	1.65677	−	0.797860i
$753$		0			0
$754$	0.327781	−	0.351721i	0.0119371	−	0.0128089i
$755$	−71.2790			−2.59411
$756$		0			0
$757$	26.2087	+	32.8647i	0.952572	+	1.19449i	0.980826	+	0.194887i	$0.0624339\pi$
$757$	26.2087	+	32.8647i	0.952572	+	1.19449i	−0.0282540	+	0.999601i	$0.508995\pi$
$758$	−0.558164	+	0.699915i	−0.0202734	+	0.0254221i
$759$		0			0
$760$	−0.0839258	−	0.0404165i	−0.00304431	−	0.00146606i
$761$	−15.8814	−	19.9147i	−0.575701	−	0.721906i	0.405672	−	0.914019i	$-0.367038\pi$
$761$	−15.8814	−	19.9147i	−0.575701	−	0.721906i	−0.981373	+	0.192113i	$0.938466\pi$
$762$		0			0
$763$	5.93804	−	26.0163i	0.214971	−	0.941852i
$764$	26.2340	−	32.8964i	0.949112	−	1.19015i
$765$		0			0
$766$	0.145427			0.00525448
$767$	4.19017	+	18.3583i	0.151298	+	0.662881i
$768$		0			0
$769$	8.17793	+	3.93828i	0.294904	+	0.142018i	0.575486	−	0.817812i	$-0.304813\pi$
$769$	8.17793	+	3.93828i	0.294904	+	0.142018i	−0.280582	+	0.959830i	$0.590527\pi$
$770$	−0.0264010	−	0.115670i	−0.000951427	−	0.00416847i
$771$		0			0
$772$	−5.81921	−	25.4956i	−0.209438	−	0.917608i
$773$	8.43552	−	10.5778i	0.303404	−	0.380457i	−0.606634	−	0.794981i	$-0.707481\pi$
$773$	8.43552	−	10.5778i	0.303404	−	0.380457i	0.910038	+	0.414524i	$0.136052\pi$
$774$		0			0
$775$	−4.58293	+	20.0791i	−0.164624	+	0.721263i
$776$	0.770213	+	0.965817i	0.0276490	+	0.0346708i
$777$		0			0
$778$	−0.497056	+	0.239370i	−0.0178203	+	0.00858182i
$779$	0.603523	−	0.756794i	0.0216234	−	0.0271149i
$780$		0			0
$781$	6.26347	−	3.01633i	0.224125	−	0.107933i
$782$	−0.0917726			−0.00328178
$783$		0			0
$784$	−14.7720			−0.527571
$785$	−35.0518	+	16.8801i	−1.25105	+	0.602476i
$786$		0			0
$787$	−20.7270	+	25.9909i	−0.738839	+	0.926474i	−0.999238	−	0.0390267i	$-0.987574\pi$
$787$	−20.7270	+	25.9909i	−0.738839	+	0.926474i	0.260400	+	0.965501i	$0.416146\pi$
$788$	−23.9360	+	11.5270i	−0.852686	+	0.410632i
$789$		0			0
$790$	−0.984782	−	1.23488i	−0.0350370	−	0.0439350i
$791$	6.89681	−	30.2169i	0.245222	−	1.07439i
$792$		0			0
$793$	−14.3022	+	17.9344i	−0.507886	+	0.636868i
$794$	−0.0152688	−	0.0668969i	−0.000541869	−	0.00237408i
$795$		0			0
$796$	−0.572608	−	2.50876i	−0.0202956	−	0.0889206i
$797$	47.2370	+	22.7482i	1.67322	+	0.805781i	0.997652	+	0.0684851i	$0.0218165\pi$
$797$	47.2370	+	22.7482i	1.67322	+	0.805781i	0.675570	+	0.737296i	$0.263898\pi$
$798$		0			0
$799$	9.82858	+	43.0618i	0.347710	+	1.52342i
$800$	2.66453			0.0942055
$801$		0			0
$802$	0.0645961	−	0.0810009i	0.00228097	−	0.00286024i
$803$	0.395115	−	1.73111i	0.0139433	−	0.0610896i
$804$		0			0
$805$	2.45767	+	3.08182i	0.0866216	+	0.108620i
$806$	0.294011	+	0.141588i	0.0103561	+	0.00498723i
$807$		0			0
$808$	−0.636465	+	0.798102i	−0.0223908	+	0.0280771i
$809$	3.86163	+	4.84233i	0.135768	+	0.170247i	0.845067	−	0.534660i	$-0.179560\pi$
$809$	3.86163	+	4.84233i	0.135768	+	0.170247i	−0.709300	+	0.704907i	$0.750989\pi$
$810$		0			0
$811$	21.7975			0.765412			0.382706	−	0.923870i	$-0.374992\pi$
$811$	21.7975			0.765412			0.382706	+	0.923870i	$0.374992\pi$
$812$	−2.87087	−	19.3332i	−0.100748	−	0.678463i
$813$		0			0
$814$	−0.0798983	+	0.0384770i	−0.00280043	+	0.00134862i
$815$	−17.2099	−	21.5805i	−0.602836	−	0.755933i
$816$		0			0
$817$	−0.487822	+	0.234923i	−0.0170667	+	0.00821890i
$818$	−0.940587	−	0.452963i	−0.0328869	−	0.0158375i
$819$		0			0
$820$	−7.75140	+	33.9611i	−0.270691	+	1.18597i
$821$	−5.69755	+	24.9626i	−0.198846	+	0.871200i	0.772780	+	0.634675i	$0.218866\pi$
$821$	−5.69755	+	24.9626i	−0.198846	+	0.871200i	−0.971625	+	0.236526i	$0.923991\pi$
$822$		0			0
$823$	−6.47616	−	28.3739i	−0.225745	−	0.989052i	−0.953068	−	0.302757i	$-0.902093\pi$
$823$	−6.47616	−	28.3739i	−0.225745	−	0.989052i	0.727323	−	0.686295i	$-0.240764\pi$
$824$	−0.772483			−0.0269107
$825$		0			0
$826$	−0.537063	−	0.258636i	−0.0186868	−	0.00899909i
$827$	9.99659	+	4.81410i	0.347615	+	0.167403i	0.599541	−	0.800344i	$-0.295350\pi$
$827$	9.99659	+	4.81410i	0.347615	+	0.167403i	−0.251926	+	0.967747i	$0.581064\pi$
$828$		0			0
$829$	9.49885			0.329909			0.164954	−	0.986301i	$-0.447252\pi$
$829$	9.49885			0.329909			0.164954	+	0.986301i	$0.447252\pi$
$830$	−0.0755942	−	0.331200i	−0.00262391	−	0.0114961i
$831$		0			0
$832$	−4.01005	+	17.5692i	−0.139024	+	0.609102i
$833$	2.87917	−	12.6145i	0.0997574	−	0.437066i
$834$		0			0
$835$	−21.6103	−	10.4070i	−0.747854	−	0.360148i
$836$	−0.165586	+	0.0797420i	−0.00572691	+	0.00275794i
$837$		0			0
$838$	−0.670946	−	0.841339i	−0.0231774	−	0.0290636i
$839$	−34.1753	+	16.4579i	−1.17986	+	0.568191i	−0.917871	−	0.396879i	$-0.870093\pi$
$839$	−34.1753	+	16.4579i	−1.17986	+	0.568191i	−0.261990	+	0.965070i	$0.584379\pi$
$840$		0			0
$841$	−27.7487	+	8.42685i	−0.956850	+	0.290581i
$842$	0.390015			0.0134408
$843$		0			0
$844$	−12.7531	−	15.9918i	−0.438978	−	0.550461i
$845$	16.0179	−	20.0858i	0.551033	−	0.690973i
$846$		0			0
$847$	17.5772	+	8.46471i	0.603958	+	0.290851i
$848$	4.04919	+	5.07753i	0.139050	+	0.174363i
$849$		0			0
$850$	−0.172888	+	0.757471i	−0.00593000	+	0.0259810i
$851$	1.83697	−	2.30348i	0.0629704	−	0.0789624i
$852$		0			0
$853$	37.8188			1.29489			0.647446	−	0.762112i	$-0.275837\pi$
$853$	37.8188			1.29489			0.647446	+	0.762112i	$0.275837\pi$
$854$	−0.161584	−	0.707946i	−0.00552930	−	0.0242254i
$855$		0			0
$856$	−1.06081	−	0.510857i	−0.0362576	−	0.0174607i
$857$	−1.36878	−	5.99703i	−0.0467568	−	0.204855i	0.946154	−	0.323717i	$-0.104933\pi$
$857$	−1.36878	−	5.99703i	−0.0467568	−	0.204855i	−0.992911	+	0.118862i	$0.962075\pi$
$858$		0			0
$859$	5.26726	+	23.0774i	0.179717	+	0.787390i	0.981760	+	0.190124i	$0.0608892\pi$
$859$	5.26726	+	23.0774i	0.179717	+	0.787390i	−0.802043	+	0.597266i	$0.796254\pi$
$860$	12.1486	−	15.2338i	0.414263	−	0.519470i
$861$		0			0
$862$	0.318401	−	1.39500i	0.0108448	−	0.0475140i
$863$	30.7366	+	38.5425i	1.04629	+	1.31200i	0.948494	+	0.316795i	$0.102607\pi$
$863$	30.7366	+	38.5425i	1.04629	+	1.31200i	0.0977924	+	0.995207i	$0.468822\pi$
$864$		0			0
$865$	69.6804	−	33.5563i	2.36920	−	1.14095i
$866$	0.890812	−	1.11704i	0.0302710	−	0.0379587i
$867$		0			0
$868$	11.9525	−	5.75601i	0.405694	−	0.195372i
$869$	−6.23502			−0.211509
$870$		0			0
$871$	−9.18852			−0.311341
$872$	−2.08809	+	1.00557i	−0.0707117	+	0.0340530i
$873$		0			0
$874$	−0.00296447	+	0.00371733i	−0.000100275	+	0.000125741i
$875$	3.38637	−	1.63079i	0.114480	−	0.0551308i
$876$		0			0
$877$	−29.1137	−	36.5074i	−0.983100	−	1.23277i	−0.972519	−	0.232825i	$-0.925203\pi$
$877$	−29.1137	−	36.5074i	−0.983100	−	1.23277i	−0.0105817	−	0.999944i	$-0.503368\pi$
$878$	0.210375	−	0.921712i	0.00709981	−	0.0311063i
$879$		0			0
$880$	4.12050	−	5.16694i	0.138902	−	0.174178i
$881$	5.58105	+	24.4522i	0.188030	+	0.823815i	0.977653	+	0.210223i	$0.0674190\pi$
$881$	5.58105	+	24.4522i	0.188030	+	0.823815i	−0.789623	+	0.613592i	$0.789724\pi$
$882$		0			0
$883$	−8.98295	−	39.3569i	−0.302300	−	1.32446i	−0.866645	−	0.498925i	$-0.833728\pi$
$883$	−8.98295	−	39.3569i	−0.302300	−	1.32446i	0.564345	−	0.825539i	$-0.309129\pi$
$884$	−14.2438	−	6.85943i	−0.479069	−	0.230708i
$885$		0			0
$886$	0.0504092	+	0.220857i	0.00169353	+	0.00741984i
$887$	11.9802			0.402254			0.201127	−	0.979565i	$-0.435540\pi$
$887$	11.9802			0.402254			0.201127	+	0.979565i	$0.435540\pi$
$888$		0			0
$889$	3.28993	−	4.12544i	0.110341	−	0.138363i
$890$	−0.310859	+	1.36196i	−0.0104200	+	0.0456530i
$891$		0			0
$892$	−9.66678	−	12.1218i	−0.323668	−	0.405867i
$893$	2.06174	+	0.992884i	0.0689937	+	0.0332256i
$894$		0			0
$895$	48.7202	−	61.0931i	1.62854	−	2.04212i
$896$	−1.42662	−	1.78893i	−0.0476601	−	0.0597639i
$897$		0			0
$898$	0.0590073			0.00196910
$899$	−11.0527	−	16.2876i	−0.368628	−	0.543221i
$900$		0			0
$901$	−5.12515	+	2.46814i	−0.170743	+	0.0822257i
$902$	−0.0667614	−	0.0837161i	−0.00222291	−	0.00278744i
$903$		0			0
$904$	−2.42524	+	1.16793i	−0.0806623	+	0.0388449i
$905$	−54.7732	−	26.3774i	−1.82072	−	0.876813i
$906$		0			0
$907$	−8.90704	+	39.0243i	−0.295753	+	1.29578i	0.580631	+	0.814167i	$0.302806\pi$
$907$	−8.90704	+	39.0243i	−0.295753	+	1.29578i	−0.876384	+	0.481613i	$0.840051\pi$
$908$	3.05853	−	13.4003i	0.101501	−	0.444704i
$909$		0			0
$910$	−0.117659	−	0.515500i	−0.00390037	−	0.0170887i
$911$	−31.8339			−1.05470			−0.527351	−	0.849647i	$-0.676815\pi$
$911$	−31.8339			−1.05470			−0.527351	+	0.849647i	$0.676815\pi$
$912$		0			0
$913$	−1.20824	−	0.581859i	−0.0399870	−	0.0192567i
$914$	−0.960479	−	0.462542i	−0.0317698	−	0.0152995i
$915$		0			0
$916$	−35.6714			−1.17862
$917$	−4.60155	−	20.1607i	−0.151957	−	0.665765i
$918$		0			0
$919$	−7.91959	+	34.6980i	−0.261243	+	1.14458i	0.658662	+	0.752439i	$0.271123\pi$
$919$	−7.91959	+	34.6980i	−0.261243	+	1.14458i	−0.919905	+	0.392142i	$0.871734\pi$
$920$	0.0761786	−	0.333760i	0.00251154	−	0.0110038i
$921$		0			0
$922$	0.552102	+	0.265878i	0.0181825	+	0.00875623i
$923$	27.9140	−	13.4427i	0.918799	−	0.442470i
$924$		0			0
$925$	−15.5518	−	19.5014i	−0.511341	−	0.641202i
$926$	−0.243479	+	0.117253i	−0.00800120	+	0.00385318i
$927$		0			0
$928$	−1.73618	+	1.86298i	−0.0569928	+	0.0611554i
$929$	7.16965			0.235229			0.117614	−	0.993059i	$-0.462475\pi$
$929$	7.16965			0.235229			0.117614	+	0.993059i	$0.462475\pi$
$930$		0			0
$931$	−0.417957	−	0.524101i	−0.0136980	−	0.0171767i
$932$	13.8597	−	17.3795i	0.453990	−	0.569285i
$933$		0			0
$934$	−1.31701	−	0.634241i	−0.0430940	−	0.0207530i
$935$	3.60917	+	4.52575i	0.118032	+	0.148008i
$936$		0			0
$937$	4.54938	−	19.9321i	0.148622	−	0.651154i	−0.844647	−	0.535323i	$-0.820190\pi$
$937$	4.54938	−	19.9321i	0.148622	−	0.651154i	0.993269	−	0.115831i	$-0.0369531\pi$
$938$	0.181355	−	0.227412i	0.00592145	−	0.00742527i
$939$		0			0
$940$	−82.3512			−2.68600
$941$	10.3898	+	45.5207i	0.338698	+	1.48393i	0.801781	+	0.597618i	$0.203886\pi$
$941$	10.3898	+	45.5207i	0.338698	+	1.48393i	−0.463083	+	0.886315i	$0.653257\pi$
$942$		0			0
$943$	3.20517	+	1.54353i	0.104375	+	0.0502641i
$944$	−7.38851	−	32.3712i	−0.240475	−	1.05359i
$945$		0			0
$946$	0.0133277	+	0.0583923i	0.000433320	+	0.00189850i
$947$	−6.36873	+	7.98614i	−0.206956	+	0.259515i	−0.874467	−	0.485086i	$-0.838788\pi$
$947$	−6.36873	+	7.98614i	−0.206956	+	0.259515i	0.667511	+	0.744600i	$0.267360\pi$
$948$		0			0
$949$	1.76088	−	7.71492i	0.0571606	−	0.250437i
$950$	0.0250974	+	0.0314711i	0.000814266	+	0.00102106i
$951$		0			0
$952$	0.902150	−	0.434452i	0.0292388	−	0.0140807i
$953$	4.18030	−	5.24193i	0.135413	−	0.169803i	−0.709501	−	0.704704i	$-0.751080\pi$
$953$	4.18030	−	5.24193i	0.135413	−	0.169803i	0.844915	+	0.534901i	$0.179651\pi$
$954$		0			0
$955$	−61.8606	+	29.7905i	−2.00176	+	0.963997i
$956$	−8.77750			−0.283885
$957$		0			0
$958$	1.08471			0.0350454
$959$	22.6922	−	10.9280i	0.732770	−	0.352884i
$960$		0			0
$961$	−10.9982	+	13.7913i	−0.354781	+	0.444881i
$962$	−0.356077	+	0.171477i	−0.0114804	+	0.00552866i
$963$		0			0
$964$	−5.40356	−	6.77585i	−0.174037	−	0.218235i
$965$	−9.49584	+	41.6040i	−0.305682	+	1.33928i
$966$		0			0
$967$	28.8734	−	36.2061i	0.928507	−	1.16431i	−0.0576234	−	0.998338i	$-0.518352\pi$
$967$	28.8734	−	36.2061i	0.928507	−	1.16431i	0.986130	−	0.165973i	$-0.0530763\pi$
$968$	−0.377031	−	1.65188i	−0.0121182	−	0.0530935i
$969$		0			0
$970$	−0.224193	−	0.982254i	−0.00719841	−	0.0315383i
$971$	−16.9355	−	8.15570i	−0.543486	−	0.261729i	0.141935	−	0.989876i	$-0.454668\pi$
$971$	−16.9355	−	8.15570i	−0.543486	−	0.261729i	−0.685421	+	0.728147i	$0.740382\pi$
$972$		0			0
$973$	−7.55262	−	33.0902i	−0.242126	−	1.06082i
$974$	−0.250494			−0.00802634
$975$		0			0
$976$	25.2190	−	31.6236i	0.807240	−	1.01225i
$977$	8.82303	−	38.6562i	0.282274	−	1.23672i	−0.612596	−	0.790396i	$-0.709875\pi$
$977$	8.82303	−	38.6562i	0.282274	−	1.23672i	0.894870	−	0.446327i	$-0.147268\pi$
$978$		0			0
$979$	3.43834	+	4.31154i	0.109890	+	0.137797i
$980$	21.7349	+	10.4670i	0.694295	+	0.334355i
$981$		0			0
$982$	0.821955	−	1.03070i	0.0262296	−	0.0328909i
$983$	13.6519	+	17.1189i	0.435426	+	0.546007i	0.950331	−	0.311240i	$-0.100744\pi$
$983$	13.6519	+	17.1189i	0.435426	+	0.546007i	−0.514905	+	0.857247i	$0.672173\pi$
$984$		0			0
$985$	43.3522			1.38132
$986$	−0.416955	−	0.614438i	−0.0132786	−	0.0195677i
$987$		0			0
$988$	−0.737955	+	0.355380i	−0.0234775	+	0.0113062i
$989$	−1.24067	−	1.55575i	−0.0394511	−	0.0494701i
$990$		0			0
$991$	11.4546	−	5.51624i	0.363867	−	0.175229i	−0.243012	−	0.970023i	$-0.578135\pi$
$991$	11.4546	−	5.51624i	0.363867	−	0.175229i	0.606879	+	0.794794i	$0.292421\pi$
$992$	−1.55730	−	0.749958i	−0.0494445	−	0.0238112i
$993$		0			0
$994$	−0.218242	+	0.956179i	−0.00692220	+	0.0303281i
$995$	−0.934386	+	4.09381i	−0.0296220	+	0.129783i
$996$		0			0
$997$	12.0266	+	52.6918i	0.380885	+	1.66877i	0.694713	+	0.719287i	$0.255532\pi$
$997$	12.0266	+	52.6918i	0.380885	+	1.66877i	−0.313827	+	0.949480i	$0.601611\pi$
$998$	0.114631			0.00362857
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.k.f.136.5	✓	60
3.2	odd	2	inner	783.2.k.f.136.6	yes	60
29.16	even	7	inner	783.2.k.f.190.5	yes	60
87.74	odd	14	inner	783.2.k.f.190.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.k.f.136.5	✓	60	1.1	even	1	trivial
783.2.k.f.136.6	yes	60	3.2	odd	2	inner
783.2.k.f.190.5	yes	60	29.16	even	7	inner
783.2.k.f.190.6	yes	60	87.74	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0355415 + 0.0171159i) q^{2} +(-1.24601 + 1.56245i) q^{4} +(2.93813 - 1.41493i) q^{5} +(1.13234 + 1.41991i) q^{7} +(0.0350984 - 0.153776i) q^{8} +(-0.0802077 + 0.100577i) q^{10} +(0.113002 + 0.495093i) q^{11} +(0.503606 + 2.20644i) q^{13} +(-0.0645483 - 0.0310848i) q^{14} +(-0.888007 - 3.89061i) q^{16} +3.49545 q^{17} +(0.112911 - 0.141586i) q^{19} +(-1.45019 + 6.35368i) q^{20} +(-0.0124902 - 0.0156622i) q^{22} +(0.599645 + 0.288774i) q^{23} +(3.51313 - 4.40532i) q^{25} +(-0.0556641 - 0.0698006i) q^{26} -3.62945 q^{28} +(0.790993 + 5.32676i) q^{29} +(-3.29319 + 1.58592i) q^{31} +(0.294840 + 0.369717i) q^{32} +(-0.124233 + 0.0598277i) q^{34} +(5.33605 + 2.56971i) q^{35} +(0.985051 - 4.31579i) q^{37} +(-0.00158966 + 0.00696476i) q^{38} +(-0.114459 - 0.501476i) q^{40} +5.34511 q^{41} +(-2.69372 - 1.29723i) q^{43} +(-0.914357 - 0.440331i) q^{44} -0.0262549 q^{46} +(2.81182 + 12.3194i) q^{47} +(0.823692 - 3.60883i) q^{49} +(-0.0494608 + 0.216702i) q^{50} +(-4.07495 - 1.96239i) q^{52} +(-1.46623 + 0.706101i) q^{53} +(1.03253 + 1.29476i) q^{55} +(0.258093 - 0.124291i) q^{56} +(-0.119285 - 0.175782i) q^{58} +8.32033 q^{59} +(6.31949 + 7.92439i) q^{61} +(0.0899006 - 0.112732i) q^{62} +(7.17412 + 3.45488i) q^{64} +(4.60162 + 5.77025i) q^{65} +(-0.903434 + 3.95820i) q^{67} +(-4.35536 + 5.46145i) q^{68} -0.233634 q^{70} +(-3.04623 - 13.3464i) q^{71} +(-3.15028 - 1.51709i) q^{73} +(0.0388584 + 0.170250i) q^{74} +(0.0805324 + 0.352836i) q^{76} +(-0.575033 + 0.721068i) q^{77} +(-2.73209 + 11.9701i) q^{79} +(-8.11401 - 10.1747i) q^{80} +(-0.189973 + 0.0914862i) q^{82} +(-1.64649 + 2.06464i) q^{83} +(10.2701 - 4.94581i) q^{85} +0.117942 q^{86} +0.0800997 q^{88} +(9.78397 - 4.71171i) q^{89} +(-2.56270 + 3.21353i) q^{91} +(-1.19836 + 0.577098i) q^{92} +(-0.310794 - 0.389723i) q^{94} +(0.131413 - 0.575760i) q^{95} +(-4.88308 + 6.12319i) q^{97} +(0.0324931 + 0.142361i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 10 q^{4} + 4 q^{7} + 4 q^{10} - 24 q^{13} - 26 q^{16} + 4 q^{19} - 8 q^{22} - 16 q^{25} + 112 q^{28} - 4 q^{31} + 26 q^{34} - 18 q^{37} - 78 q^{40} - 8 q^{43} + 72 q^{46} + 14 q^{49} - 12 q^{52}+ \cdots + 8 q^{97}+O(q^{100}) \) 60 * q - 10 * q^4 + 4 * q^7 + 4 * q^10 - 24 * q^13 - 26 * q^16 + 4 * q^19 - 8 * q^22 - 16 * q^25 + 112 * q^28 - 4 * q^31 + 26 * q^34 - 18 * q^37 - 78 * q^40 - 8 * q^43 + 72 * q^46 + 14 * q^49 - 12 * q^52 + 24 * q^55 - 162 * q^58 - 10 * q^61 + 116 * q^64 + 60 * q^67 - 12 * q^70 + 66 * q^73 - 120 * q^76 + 46 * q^79 - 84 * q^82 - 122 * q^85 - 152 * q^88 - 30 * q^91 - 68 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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